Can Majorana Fermions correctly describe the ordered state of an antiferromagnetic Heisenberg chain?

TL;DR

This paper evaluates the effectiveness of the Majorana fermion representation for quantum spin chains by comparing its predictions to exact solutions, revealing significant discrepancies and emphasizing the importance of gauge considerations.

Contribution

It provides a critical assessment of the Majorana representation's accuracy in describing antiferromagnetic spin chains, highlighting the need for careful gauge handling.

Findings

Small one-loop correction to mean field energy

Discrepancy >100% with Bethe Ansatz results

Gauge degrees of freedom are crucial for accurate results

Abstract

To check the reliability of the Majorana representation of quantum spin systems, we use it to compute the ground state energy of an antiferromagnetic spin 1/2 chain to one loop order. We find a very small one loop correction of the mean field energy and a discrepancy of >100% compared to the Bethe Ansatz result. We conclude that a careful handling of the gauge degrees of freedom of this representation is crucial to get correct results.